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Beliebt Funktionen >

extreme f(x)=x^2*ln(x)

Lösung

extrempunkte

f (x) = x^{2} \cdot ln (x)

Lösung

Minimum (\frac{1}{e}, - \frac{1}{2 e})

Schritte zur Lösung

f^{'} (x) = 2 x ln (x) + x

Intervalle finden:

Absteigend

: 0 < x < \frac{1}{e},

Ansteigend

: \frac{1}{e} < x < \infty

Stecke

x = \frac{1}{e}

in

x^{2} \cdot ln (x) : - \frac{1}{2 e}

Minimum (\frac{1}{e}, - \frac{1}{2 e})

Graph

Beliebte Beispiele

extreme 3x^{2/3}-2x,-1<= x<= 1

e x t re m e 3 x^{\frac{2}{3}} - 2 x, - 1 \leq x \leq 1

extreme f(x)=-25(x-9)^2+200

e x t re m e f (x) = - 25 (x - 9)^{2} + 200

extreme f(x)=-x^3+3x-10

e x t re m e f (x) = - x^{3} + 3 x - 10

extreme y=4x+4sin(x)

e x t re m e y = 4 x + 4 sin (x)

extreme f(x,y)=x^3+y^3-147x-75y-10

e x t re m e f (x, y) = x^{3} + y^{3} - 147 x - 75 y - 10